Quantum Nonlinear Optics with a Germanium-Vacancy Color Centerin a Nanoscale Diamond Waveguide

M. K. Bhaskar,1, ∗ D. D. Sukachev,1, 2 A. Sipahigil,1 R. E. Evans,1 M. J. Burek,3 C. T. Nguyen,1

L. J. Rogers,4 P. Siyushev,4 M. H. Metsch,4 H. Park,5 F. Jelezko,4 M. Loncar,3 and M. D. Lukin1, †

1Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA2P. N. Lebedev Physical Institute of the RAS, Moscow 119991, Russia

3John A. Paulson School of Engineering and Applied Sciences,Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA

4Institute for Quantum Optics, University Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany5Department of Chemistry and Chemical Biology, Harvard University,

12 Oxford St., Cambridge, Massachusetts 02138, USA

We demonstrate a quantum nanophotonics platform based on germanium-vacancy (GeV) color centers infiber-coupled diamond nanophotonic waveguides. We show that GeV optical transitions have a high quantumefficiency and are nearly lifetime-broadened in such nanophotonic structures. These properties yield an efficientinterface between waveguide photons and a single GeV without the use of a cavity or slow-light waveguide. Asa result, a single GeV center reduces waveguide transmission by 18 ± 1% on resonance in a single pass. Weuse a nanophotonic interferometer to perform homodyne detection of GeV resonance fluorescence. By probingthe photon statistics of the output field, we demonstrate that the GeV-waveguide system is nonlinear at thesingle-photon level.

Efficient coupling between single photons and coherentquantum emitters is a central element of quantum nonlinearoptical systems and quantum networks [1–3]. Several atom-like defects in the solid-state are currently being exploredas promising candidates for the realization of such systems[4, 5], including the nitrogen-vacancy (NV) center in dia-mond, renowned for its long spin coherence at room temper-ature [6]; and the silicon-vacancy (SiV) center in diamond,which has recently been shown to have strong, coherent opti-cal transitions in nanostructures [7–10]. The remarkable opti-cal properties of the SiV center arise from its inversion sym-metry [11], which results in a vanishing permanent electricdipole moment for SiV orbital states, dramatically reducingtheir response to charge fluctuations in the local environment.A large family of color centers in diamond are predicted tohave inversion symmetry [12] and therefore may be expectedto have similarly favorable optical properties. In this Letter,we demonstrate an efficient optical interface using negatively-charged germanium-vacancy (GeV) color centers integratedinto nanophotonic devices with properties that are superior tothose of both NV and SiV centers. These properties result inhigh interaction probabilities between individual GeV centersand photons in a single-pass configuration, even without theuse of cavities or other advanced photonic structures.

The GeV center is a new optically active color center in di-amond [13–16]. Its calculated structure, shown in Fig. 1(a), issimilar to that of the SiV center with D3d symmetry [12, 14].The Ge impurity occupies an interstitial site between two va-cancies along the 〈111〉 lattice direction [12, 14, 15], resultingin inversion symmetry. Fig. 1(b) depicts the electronic levelstructure of the GeV [14, 15] with a zero-phonon line (ZPL)transition at 602 nm which constitutes about 60% of the to-tal emission spectrum [13]. Similar to the negatively-charged

∗ mbhaskar@g.harvard.edu† lukin@physics.harvard.edu

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FIG. 1. (a) Molecular structure of the GeV center. (b) Photolumi-nescence spectrum of the GeV at T = 50 K, revealing the four opti-cal transitions predicted by the GeV electronic structure (inset) [13].∆1−2 = 152 GHz and ∆3−4 = 981 GHz are the measured groundand excited state orbital splittings respectively. The solid curve is afit to four Lorentzians.

SiV center [11, 17], the ground state of the GeV center is aspin-doublet (S = 1/2) [18] with double orbital degeneracy.The ground and excited orbital states of the GeV are splitby spin-orbit coupling, forming a four-level system visiblein its cryogenic photoluminescence (PL) spectrum [Fig. 1(b)][13, 15, 16]. As demonstrated in the complementary Letter[18], this electronic structure allows one to directly controlboth orbital and electronic spin degrees of freedom using op-tical and microwave fields.

We achieve efficient coupling of individual GeV cen-ters with single photons by incorporating them into one-dimensional waveguides [Fig. 2(a)] with transverse dimen-sions on the order of the single-atom scattering cross-section[8, 20–22]. Waveguides have a width of 480 nm, and arenanofabricated from diamond [23]. GeV centers are incor-porated into devices at low density using 74Ge+ ion implan-tation (109 Ge+ cm−2) and subsequent high temperature an-nealing at 1200 ◦C, leading to spatially-resolvable single emit-ters [7, 14]. We couple a single-mode tapered optical fiber

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FIG. 2. (a) Schematic of a diamond nanophotonic device. Devices are 100 µm long and 480 nm wide and consist of a waveguide (red box),a partially-reflective Bragg mirror (purple box), and a taper (black box) for coupling to a tapered single-mode optical fiber. (b) Saturationresponse for a single GeV under continuous-wave, 520 nm excitation at T = 300 K, measured as a function of optical power at the microscopeobjective. The solid curve is a fit to a two-level saturation model [19]. (c) Intensity autocorrelation demonstrates antibunching of g(2)(0) =0.08 ± 0.02. The solid curve is a single-exponential fit. (d) GeV excited state lifetime measurement at different temperatures in waveguides(red) and bulk diamond (blue). Error bars represent standard deviation of measured lifetimes of seven different emitters. For T > 300 K, thelifetime was measured for a single GeV in a waveguide (red diamonds).

to the waveguide with ∼ 50% coupling efficiency by posi-tioning it in contact with a tapered section of the diamond[8, 24, 25]. We implement this technique under a confocalmicroscope (described in [8, 19]), enabling both free-spaceand fiber-based collection of fluorescence from GeV centers.

We first measure the ZPL emission of a single GeV in awaveguide under continuous-wave 520 nm off-resonant exci-tation at room temperature [Fig. 2(b)]. Collecting via the ta-pered fiber, we observe a maximum single-photon detectionrate of 0.56 ± 0.02 Mcps (million counts per second) on thenarrowband ZPL around 602 nm, limited by excitation laserpower. The single-photon nature of the emission is verifiedby antibunching of ZPL photons [Fig. 2(c)], measured atI/Isat ∼ 0.5 where I and Isat (4.7 ± 0.2 mW at 520 nm)are applied and saturation intensities respectively. To betterunderstand the optical properties of the GeV, we measure itsexcited state lifetime at different temperatures with 532 nmpulsed excitation [Fig. 2(d)]. The GeV lifetime does not dis-play significant temperature dependence up to T = 450 K atwhich local vibrational modes with∼ 60 meV energy [13, 15]have finite occupation. This demonstrates that phonon pro-cesses play a negligible role in determining the excited statelifetime [26] and that the radiative quantum efficiency is closeto unity. A statistically significant difference in lifetime forwaveguide (6.6± 0.3 ns) and bulk (6.0± 0.1 ns) emitters im-plies a high sensitivity to the local photonic density of states[27], providing further evidence of a high radiative quantumefficiency.

To study coherence properties of single GeV centers in awaveguide, we use resonant excitation on transition 1-3 [Fig.1(b)] at T = 5 K. We scan the frequency of the laser over theGeV resonance and record the fluorescence in the phonon-sideband (PSB) collected into the tapered fiber. This tech-nique yields a linewidth of 73± 1 MHz after 5 minutes of av-eraging at low excitation intensity [Fig. 3(a)]. The measured

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FIG. 3. (a) Transition 1-3 linewidth of a GeV in a waveguide at T =5 K, taken under resonant excitation at I/Isat ∼ 0.01. The solidcurve is a Lorentzian fit. (Inset) Linewidth as a function of temper-ature, PL spectrum measured on a spectrometer under 520 nm exci-tation. Different colored points correspond to different emitters. Thesolid curve is a fit to a T 3 model [19]. (b) Optical Rabi oscillations.Fluorescence is measured on the PSB under resonant excitation. Thesolid curves are fits to a two-level model [19]. (Inset) The Rabi oscil-lation decay rate scales linearly as a function of temperature for T <10 K.

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FIG. 4. (a) Schematic for single-pass transmission measurement.The resonant excitation (I/Isat ∼ 0.02) is focused on the Braggmirror to scatter light into the waveguide. We collect transmittedlight into the tapered optical fiber and subsequently separate the ZPLand PSB using a bandpass filter. (b) Transmission spectrum of theGeV-waveguide device, showing 18 ± 1% extinction on resonance.ZPL transmission is shown on top (right axis) in orange and PSBfluorescence is shown on the bottom (left axis) in red. The solidcurves are Lorentzian fits.

linewidth of a GeV in a nanophotonic structure is within afactor of 3 of the lifetime-broadened limit, γ0/(2π) = 26± 1MHz [19]. The measured linewidth increases with temper-ature up to T = 300 K [inset of Fig. 3(a)], due to phononbroadening that scales as a+ b(T − T0)3 [a = 0.0± 0.2 nm,b = (1.9 ± 0.5) × 10−7 nm K−1, T0 = (−13 ± 23) K] forT > 50 K. The T 3 scaling suggests that optical coherence islimited by a two-phonon orbital relaxation process for T >50 K, similar to the case of the SiV [26].

In Fig. 3(b) we demonstrate coherent control over the GeVoptical transition 1-3 by applying a resonant 40-ns pulse andobserving optical Rabi oscillations using photons detected onthe PSB. At high excitation power, the GeV optical transi-tion undergoes spectral diffusion of roughly 300 MHz aboutthe original resonance frequency. In order to mitigate spectraldiffusion at high excitation intensities, we use an active feed-back sequence [28, 29] that stabilizes the GeV resonance fre-quency while maintaining a high duty cycle on resonance [19].This procedure enables high contrast oscillations at a Rabi fre-quency of 310 ± 2 MHz with a decay time of 6.59 ± 0.02 nsat 5 K, close to the excited state lifetime of 6.1 ± 0.2 ns. Thedecay rate of Rabi oscillations increases linearly with tem-perature [inset in Fig. 3(b)], suggesting that a single-phononorbital relaxation process limits optical coherence at low tem-peratures between T = 5 K and T = 10 K, again similar tothe case of the SiV [26].

These excellent optical properties allow us to observe theextinction of resonant transmission through a single GeV cen-ter in a waveguide, as demonstrated in Fig. 4. We focus theexcitation on the Bragg mirror in order to scatter laser lightinto the waveguide. We collect the light transmitted through

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FIG. 5. (a) Schematic for homodyne interferometer. We excite(I/Isat ∼ 0.02) and collect through two ports of a fiber beamsplit-ter (BS). We use polarization paddles to change the excitation po-larization. (b) Homodyne interfererometry with a single GeV. TheZPL signal is shown on top (right axis) at two different input po-larizations (orange and blue). PSB fluorescence is shown on thebottom (left axis) in red. The solid red curve is a Lorentzian fitand the solid blue and orange curves are fits to a phenomenologicalmodel [19]. (c) Autocorrelation measurement. We perform HanburyBrown-Twiss interferometry on the ZPL output field in the case ofdestructive interference for single photons. We measure bunching ofg(2)(0) = 1.09 ± 0.03 with a decay time τb = 6.2 ± 2.7 ns. Thesolid curve is an exponential fit [19].

the GeV into the tapered fiber, separating the ZPL (transmis-sion) and PSB (fluorescence) components using a bandpassfilter [Fig. 4(a)]. We find that on resonance, a single GeV re-duces waveguide transmission by 18 ± 1% [Fig. 4(b)]. Theextinction of resonant light by a single quantum emitter isan effective measure of the strength of emitter-photon inter-actions, and is related to the emitter-waveguide cooperativityC = Γ1D/Γ

′, the ratio of the decay rate into the waveguideΓ1D, to the sum of atomic decay rates to all other channels anddephasing Γ′ [20, 21]. From the measured extinction from asingle GeV, we directly obtain the GeV-waveguide cooperativ-ity of C ≥ 0.10±0.01 [19]. Because the GeV is a multi-levelsystem with finite thermal population in level 2 at T = 5 K,the cooperativity extracted from transmission of light resonant

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with transition 1-3 is a lower bound and can be improved byinitializing the GeV in state 1 by optical pumping [8].

The extinction of resonant light results from destructive in-terference between the driving field (a local oscillator) andresonance fluorescence from the GeV, and in general dependson the relative phase between them [30]. This phase can becontrolled in a homodyne measurement involving a laser fieldand GeV resonance fluorescence in the stable nanophotonicinterferometer depicted in Fig. 5(a). Here, the laser light isinjected through one port of a fiber beamsplitter connected tothe tapered fiber and collected via a second beamsplitter port.The output field at ZPL wavelengths consists of interferencebetween GeV resonance fluorescence and the near-resonantexcitation laser light reflected back into the fiber by the Braggmirror, which acts as a local oscillator. We vary the rela-tive amplitude and phase of the local oscillator with respectto the GeV resonance fluorescence by modifying the polar-ization of input laser light (for details, see [19]). Using thistechnique, we observe the change in lineshape of the outputlight from symmetric, corresponding to destructive interfer-ence (orange), to dispersive (blue) [Fig. 5(b)].

Finally, Fig. 5(c) demonstrates the quantum nonlinear char-acter of the coupled GeV-waveguide system. In the homodynemeasurement, the local oscillator is a weak coherent state withnon-negligible single and two-photon components, whereasthe GeV resonance fluorescence consists of only single pho-tons. In the case of large single atom-photon interaction prob-ability, a single photon in the waveguide mode can saturate theGeV center and a single GeV can alter the photon statistics ofthe output field [20]. As an example, in the case of destructiveinterference between the two fields, the output field consistspreferentially of two-photon components from the local os-cillator, resulting in photon bunching. We probe the photonstatistics of the homodyne output field using Hanbury Brown-Twiss interferometry and observe, in the case of destructiveinterference, g(2)(0) = 1.09 ± 0.03 [Fig. 5(c)]. This obser-vation provides direct evidence of device nonlinearity at thelevel of a single photon [8, 20, 22].

We next turn to the discussion of our experimental obser-vations. The GeV excited state lifetime [Fig. 2(d)] sets a the-oretical upper bound on the single-photon flux from a GeVcenter of roughly 160 Mcps. From the saturation curve in Fig.2(b), we infer that the maximum possible ZPL single-photondetection rate is 0.79 ± 0.02 Mcps in our experiment. Ac-counting for the ZPL branching ratio and setup inefficiencies,we estimate that per excitation, the probability of emission ofa photon into the waveguide mode is at least 0.1 [19]. Thesemeasurements demonstrate that a single GeV center in a dia-mond waveguide is an efficient source of narrowband singlephotons.

The cooperativity measured in the transmission experiment(Fig. 4) is reduced by a combination of line-broadening mech-anisms and multi-level dynamics [8, 20]. Since the branchingratios of the GeV optical transitions are not yet known, it isdifficult to develop a comprehensive model of the populationdynamics. Using a simple three-level model, we estimate thephonon relaxation rate using γp = 2γRabi − 3

2γ0 [29], whereγRabi is the decay rate of Rabi oscillations, and γ0 (γp) is the

excited state (phonon) relaxation rate. Using the measuredvalue of γRabi/(2π) = 24 ± 0.1 MHz from Fig. 3(b), weinfer that phonon relaxation leads to γp/(2π) = 9 ± 2 MHzof Markovian line-broadening at T = 5 K. Therefore, the ob-served 73 MHz linewidth is limited at 5 K by a combinationof phonon relaxation and residual spectral diffusion and canlikely be reduced further at lower temperatures, as demon-strated for GeV centers in bulk diamond [18].

The present observations, together with recent advances in-volving SiV centers [8], demonstrate significant potential forthe realization of quantum nanophotonic devices using thefamily of color centers in diamond with inversion symmetry[12]. The negatively-charged GeV center investigated herealso has an electronic spin (S = 1/2) degree of freedom thatcan be manipulated using optical and microwave fields, mak-ing it a promising spin-photon interface [18]. As in the caseof the SiV, coherence between GeV orbital and spin sublevelsis limited by phonon relaxation at finite temperatures. On-going efforts to suppress these relaxation processes at lowertemperatures should result in long spin coherence times [26].

Our observations also point to some key differences in theoptical properties of GeV and SiV centers. In particular, theGeV excited state lifetime [Fig. 2(d)] shows negligible tem-perature dependence and high sensitivity to changes in the lo-cal photonic density of states, indicating the primarily radia-tive nature of the decay. By contrast, the excited state life-time of the SiV has strong temperature dependence [26] anddoes not respond as sensitively to changes in the local pho-tonic density of states [7]. These observations demonstratethat the GeV has a significantly higher quantum efficiencythan the SiV. Such a high quantum efficiency directly resultsin the strong extinction of light by a single GeV in a single-pass, without the need for a slow-light waveguide or cavity.In particular, the extinction observed here appears to exceedthat of any other comparable single-pass transmission exper-iment, including those using single trapped atoms [31], ions[32], molecules [33], and quantum dots [34].

These observations open up exciting prospects for the real-ization of coherent quantum optical nodes with exceptionallystrong atom-light coupling. In particular, the high quantumefficiency of the GeV, when integrated into diamond nanocav-ities with previously demonstrated quality factor-mode vol-ume ratios Q/V > 104 [23, 24], could enable device co-operativities C > 100, leading to deterministic single atom-photon interactions. GeV orbital and spin coherence proper-ties can be improved by cooling devices below 1 K, potentiallyyielding long-lived quantum memories [26]. Arrays of suchstrongly-coupled GeV-nanophotonic devices could be used asa basis for the realization of integrated quantum optical net-works with applications in quantum information science [1]and studies of many-body physics with strongly interactingphotons [3].

We thank D. Twitchen and M. Markham from Element SixInc. for substrates and C. Meuwly and M. Goldman for ex-perimental help. Financial support was provided by the NSF,the CUA, the AFOSR MURI, the ONR MURI, the DARPAQuINESS program, the ARL, and the Vannevar Bush Fac-ulty Fellowship program. F.J. is affiliated with the Center

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for Integrated Quantum Science and Technology (IQst) in BadenWurttemberg, Germany. Devices were fabricated at theHarvard CNS supported under NSF award ECS-0335765.

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